Mathematical Sciences: Shimura Varieties and Endoscopy

Kottwitz教授将研究几个与自同构形式有关的问题。特别是，他将研究内窥镜及其在志村品种上的应用。他还将研究Arthur的稳定型示踪公式、志村变元的不良约简问题以及稳定型示踪公式与Lefschetz不动点公式之间的联系。自同构形式产生于19世纪中期的非欧几里得几何。因此，数学家和物理学家很早就认识到，许多具有根本重要性的物体在其基本性质上是非欧几里得的。这个领域主要关注关于整数的问题，但在使用几何和分析时，它保留了与历史根源的联系，因此与理论物理中的规范理论和信息论中的编码理论等领域的问题联系在一起。

Professor Kottwitz will work on several problems connected with automorphic forms. In particular, he will study endoscopy and its applications to Shimura varieties. He will also work on the stable version of Arthur's trace formula, problems of bad reduction of Shimura varieties and connections between the stable trace formula and the Lefschetz fixed point formula. Automorphic forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.